The Number of Rakaats for Tahajjud prayer?

What is the minimum and maximum number of Rakaats for Tahajjud prayer? And also what is beginning and ending times for Tahajjud ? Related to Tahajjud please also answer the following.

A. If one wakes up at 2 AM and prays Tahajjud and then goes back to sleep again to wake up at Fajr, will his Tahajjud be valid and acceptable

B. If one wakes up at 4:30 AM and prays Tahajjud and then keeps awake until 5:30 AM which is the time of Fajr, then prays Fajr and goes back to sleep, will his Tahajjud be counted as valid and acceptable?

A-3

Alhamdulillah wassalatu wassalamu ala ashrafa rasulillah

The better way to perform Tahajjud prayer is that one should sleep little bit after Esha prayer then wake up and perform ( two to eight or twelve rakaats of prayers) that will be considered Tahajjud prayer.But the preferred time to perform Tahajjud is the last third (part) of the night because this is the time in which mercy of Allah comes closer to the servant. Here are two hadiths in support of the above mentioned statement:

Allah's Messenger peace be upon him said, "Our Lord, the Blessed, the Superior, comes down (coming down of Lord means "His mercy becomes closer to the creation, as our Lord does not have any form, shape or body to come down in His body form") every night to the nearest heaven from us when the last third of the night remains. Saying: "Is there anyone to invoke Me, so that I may respond to his invocation? Is there anyone to ask Me, so that I may grant him his request? Is there anyone to seek My forgiveness, so that I may forgive him?"

It was narrated by Abd Allah bin Amr said: the Messanger of Allah said: the prayer which is dearest to Allah is that of Prophet Dawood and the fasting which is dearest to Allah is that of Prophet Dawood, he used to sleep half of the night, get up to offer prayer for one third of it, then sleep through the remaining one-sixth of it. And he used to observe fast on alternate days.

According to the Hadith the minimum number of Rakaats for Tahajjud prayer is two and the maximum number is eight as it is as mentioned in Fathul Qadir1/447

The answer for both A & B is that his Tahajjud in both situations is acceptable and valid.